When not to rely on the central limit theorem - an example from absenteeism data

Abstract

When sampling from a skew distribution, one often assumes that the robustness of the one- and two-sample t-tests ensures their accuracy for a 'reasonably large' sample size. An example from absenteeism (days lost per annum) serves to illustrate the fallacy of this assumption even for quite large samples (e.g. 500) especially for single sample estimation and testing. The two-sample t-test appears somewhat more robust provided the two samples are of approximately equal size.